According to the disclosure in Swiss Pat. No. 548,764, the sedimentation rate of red blood cells is determined according to the Westergren method by placing a 200 mm blood column in a transparent tube. Subsequently, the tube upper end is sealed with an inserted stopper which is used simultaneously for zero point adjustment and for suspension of the sedimentation tube in a holding apparatus. As such tubes are filled using syringes whose pistons slide unevenly or with a jerky movement, blood is unintentionally squirted or splashed out of the tube end. People, particularly those who carry out a multiplicity of blood examinations, are thereby exposed to the danger of infection by contaminated blood.